Identify the error in the following proof. Why is this an error? If the statemen
ID: 3028363 • Letter: I
Question
Identify the error in the following proof. Why is this an error? If the statement is true, correct and rewrite the proof. Highlight the correction and explain your reasoning for addressing the problem in way. If the statement is false or cannot be proven, explain why you reached this conclusion. Statement: Prove, or disprove by finding a counterexample: if f is continuous on (a, b), then f is bounded on (a, b). Counterexample: f(x) = x is continuous but unbounded, therefore the statement is false.|Explanation / Answer
Sol. If f is continuous on (a, b) then it may not be bounded. For eg. f(x)=1/x or f(x)=x^2 are continuous on (0,1) but unbounded. But f(x)=x is continuous as well as bounded on (0,1) but infimum of f is 0 and suprimum is 1.